In politics you are really only relevant so long as you are solving people’s problems.
A truism lost on Mrs May and Jeremy Corbyn.
For if Mrs May was consumed with creating difficulties, the Labour leader was busy demonstrating a deft fleetness of foot running from them.
Having butted heads and traded insults for nigh on three years, Mrs May has been coerced by an ominously ticking clock to extend the hand to Mr Corbyn to join her on the flaming deck.
It might be the only sensible move she has made since triggering Article 50. But fears their union will be barren are justified. Given his record, it is hard to see how Mr Corbyn could bring himself to vote for anything Mrs May proposes.
His “I never kissed a Tory” mantra does not bode well for a fruitful relationship. Yet in the game of change you get nowhere if you are not in the race, so Mr Corbyn must show willing.
While both may be out of time, neither will want to carry the brunt for a no-deal crash out.
Labour supporters will expect Mr Corbyn to wring a second referendum from Mrs May, and block any deal that comes without a public vote.
But agreeing to a referendum, or joining a customs union, would breach the prime minister’s infamous red lines.
Appealing for more time from Brussels without putting something meaningful on the table won’t wash.
At this stage, to cheat the public of the chance of an orderly Brexit only to further their own ends would render both irredeemable political failures.
In one sense they deserve no less. If Mrs May’s culpability lies in investing all her energies in stopping the Tories from imploding – even as they devoured each other – Corbyn’s sin was as grievous; standing idly by as one vote after another went up in smoke, wilfully destroying all chance of consensus.
His ultimate plan to steal an election from the ashes is opportunistic and self-serving, given the enormity of what is at stake.
Regardless how it came about, this 11th-hour shot at redemption to finally restore the primacy of the national interest before their respective party agendas must be seized.
After all the exhausting theatrics it looks as if the whole matter could yet be settled on the toss of a coin. Heads it’s Mrs May’s plan; tails gives us a Labour Brexit – providing the House agrees. And holding one’s breath on that outcome would be ill-advised. Even so, having blundered through so many critical deadlines to date, it has to be hoped both leaders can rise to the occasion to spare theirs and their country’s blushes.
But should Brussels grant them extra time, it must be used constructively to restore some dignity. Westminster has looked more Mrs Brown than the Mother of all Parliaments of late. Something other than snubbing disdainful noses at the rest of the bloc is not too much to demand.